Depreciation/Rate of Change (Calculus I)

Problem: The value of a piece of machinery depreciates exponentially. When purchased new, it was worth $70,000. After 4 years, it was worth $55,200. Find the rate of change of the value of the equipment after 4 years.

The value of a piece of machinery depreciates exponentially.
When purchased new, it was worth $70,000. After 4 years, it was worth $55,200.
Find the rate of change of the value of the equipment after 4 years.

We have: .

When

Then: .

Hence: .

. . The function is: .

The rate of change is: .

When

At the end of 4 years, it is depreciating at the rate of $3261.79 per year.